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**Mohamed A. Abdel-Razek**

Department of Mathematics, Faculty of Science, Assiut University,

Assiut 71516, Egypt

**Ayman M. Mahmoud**

Department of Mathematics, Faculty of Science,

New Valley University, El-Khargah 72511, Egypt

**Doaa A. M. Bakhit**

Department of Mathematics, Faculty of Science,

New Valley University, El-Khargah 72511, Egypt

This paper investigates the explicit criteria of the stability of the zero solution and the boundedness of all solutions for a certain non-autonomous third-order functional differential equation with multiple deviating arguments. To study the stability of the zero solution we construct the Lyapunov functional. The Gronwall-Reid-Bellman inequality is employed to establish the boundedness of all solutions of the addressing model. This study includes and improves some related results existing in the relevant literature. For illustration, two examples are given.

- boundedness
- functional
- functional differential equations
- Lyapunov
- multiple deviating arguments
- stability
- third-order differential equation

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